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On Hormander's solution of the -equation. I
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-4971-7147
2015 (English)In: Mathematische Zeitschrift, ISSN 0025-5874, E-ISSN 1432-1823, Vol. 281, no 1-2, 349-355 p.Article in journal (Refereed) Published
Abstract [en]

We explain how Hormander's classical solution of the -equation in the plane with a weight which permits growth near infinity carries over to the rather opposite situation when we ask for decay near infinity. Here, however, a natural condition on the datum needs to be imposed. The condition is not only natural but also necessary to have the result at least in the Fock weight case. The norm identity which leads to the estimate is related to general area-type results in the theory of conformal mappings.

Place, publisher, year, edition, pages
2015. Vol. 281, no 1-2, 349-355 p.
Keyword [en]
(partial derivative)over-bar-Equation, Weighted estimates (partial derivative)over-bar-equation, Hormander's theorem, Growing weight, Existence, Uniqueness of the solution
National Category
URN: urn:nbn:se:kth:diva-173413DOI: 10.1007/s00209-015-1487-7ISI: 000359830400014ScopusID: 2-s2.0-84939575144OAI: diva2:853821

QC 20150915

Available from: 2015-09-15 Created: 2015-09-11 Last updated: 2015-09-15Bibliographically approved

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Hedenmalm, Håkan
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